An article gave the data, shown in the table below, on dimensions of 27 representative food products. Maximum Minimum Width Width Product 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 Material Height glass glass glass glass plastic glass glass plastic plastic plastic tin plastic glass glass glass glass cardboard. cardboard glass glass glass glass glass glass plastic tin tin 7.7 6.2 8.5 10.4 8.0 8.7 10.2 10.5 3.4 6.9 10.9 9.7 10.1 13.0 13.0 11.0 8.7 17.1 16.5 16.5 9.7 17.8 14.0 13.6 27.9 19.5 13.8 2.50 2.90 2.15 O Ho: at least one of B₁, B₂ or 3 is not 0 H₂: B₁ = B₂= B₂ = 0 2.90 Ho: B₁, B₂ and 3 are all not 0 H₁: B₁ B₂ =B3 = 0 3.20 2.00 1.60 4.80 5.90 5.80 2.90 2.45 2.60 2.60 2.70 3.10 5.10 10.20 3.50 2.70 3.00 2.70 2.50 2.40 4.40 7.50 4.25 (c) Carry out a model utility F test at a 0.05 significance level. State the null and alternative hypotheses. Ho: B₁ = B₂ = ß3 = 0 H: B₁, B₂ and ₂ are all not 0 1.80 Ho: B₁ = B₂ = ß₂3 = 0 H: at least one of B₁, B₂ or 3 is not 0 2.70 2.00 2.60 3.15 1.80 1.50 3.80 5.00 4.75 2.80 2.10 2.20 2.60 2.60 2.90 5.10 10.20 3.50 1.20 1.70 1.75 1.70 1.20 1.20 7.50 4.25 Elongation 1.50 1.07 Calculate the test statistic. (Round your answer to two decimal places.) F = 1.98 1.79 1.25 2.17 3.19 1.09 0.29 0.59 1.88 1.98 1.94 2.50 2.41 1.77 0.85 0.84 2.36 3.06 1.62 3.30 2.80 2.83 3.17 1.30 1.62 Volume 130 139 Use technology to calculate the P-value. (Round your answer to four decimal places.) P-value= 180 281 332 93 119 515 325 568 339 180 235 239 363 312 631 1248 651 306 320 310 (a) Fit a multiple regression model for predicting the volume (in ml) of a package based on its minimum width, maximum width, and elongation score. (Round your numerical values to two decimal places. Use x₁ for minimum width, x₂ for the maximum width and x3 for the elongation score.) ŷ = 247 (b) Why should we consider adjusted R² instead of R2 when evaluating this model? O We should consider the adjusted ² instead of r² because it takes into account the number of predictors used in the model. In this case the adjusted ² is noticeably less than ². O We should consider the adjusted ² instead of r² because it does not take into account the number of predictors used in the model. In this case the adjusted ² is noticeably greater than 2. O We should consider the adjusted ² instead of 2 because it takes into account the number of predictors used in the model. In this case the adjusted 2 is noticeably greater than ². O We should consider the adjusted ² instead of r² because it does not take into account the number of predictors used in the model. In this case the adjusted r² is noticeably less than ². 204 1204 2329 731